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Forum:Joyce's More Generalized Exponential Notation
I don't understand the rules of this function. Can we clean them up? I know g(n,n+1,n,2) = mag(n) = gag^n(n) but I cant see that in the article. Wythagoras (talk) 07:40, August 1, 2013 (UTC) Rules don't specify what to do if a=1. I believe we chop leading 1's, but rules don't say that. LittlePeng9 (talk) 08:16, August 1, 2013 (UTC) It's also odd how this linear array notation can express trimentri using g(g(2, g(2, 3, 3), 3), 1, 1, 4, 3, 3), as it stated in the source. Ikosarakt1 (talk ^ ) 08:24, August 1, 2013 (UTC) It can't and it doesn't. Turns out that g(g(2,g(2,3,3),3),1,1,4,3,3) = g(3^3^3,1,1,4,3,3) ~ G(7,625,597,484,987). So not even CLOSE! Joyce does not understand how array notation works. He has severely underestimated it. It's about time Joyce got knocked off his high horse. He has nothing on Bowers. Sbiis Saibian (talk) 20:14, April 23, 2014 (UTC) :Bowers 1 :Joyce 0 you're.so. 07:43, April 24, 2014 (UTC) lel WikiRigbyDude (talk) 20:34, April 23, 2014 (UTC) Joyce's day of "reckoning" (number pun intended) has finally arrived! I finally finished my analysis of Joyce's work and published a new article about it on my site (see update panel). The Final Assessment: Joyce doesn't even manage to reach a grand tridecal, {10,10,10,2} , even under generous assumptions, and the order-type of the polyadic g-function can not exceed w*2, and might be as small as w+2 (depending on how you interpret the continuation of the g-function to arbitrary arguments as detailed in the article ). I hope this vindicates Bowers' work in some small way P.S. I have dubbed Joyce's attempt to compute Bowers' array notation as "the most epicly EPIC fail in all of googology history" :) Sbiis Saibian (talk) 02:22, April 30, 2014 (UTC) I got a good laugh out of Saibian's new article c: WikiRigbyDude (talk) 17:40, April 30, 2014 (UTC) When I only started to learn about googology, I met the article describing Joyce's rules, and even then they, purely intuitively, seemed to me so disgusting because they had lack of definitions past 6-entries (why stop at 6?), terminating rules and general arbitrariness of them. I just skipped it and went to Bowers' notation after learning about up-arrows and G function. Now I see clearly that I lost nothing. Ikosarakt1 (talk ^ ) 19:07, April 30, 2014 (UTC) Update: The article now includes a reference table towards the bottom, that lists the most relevant Joycian googolism's in size order, along with Bowerism's for size reference. Turns out the smallest Bowerian googologism to exceed all of Joyce's numbers is a corporalplex. In fact Joyce's googolism's can be bound by {3,3,2,2} Sbiis Saibian (talk) 21:43, April 30, 2014 (UTC) SI prefixes I see you had a little trouble figuring out Joyce's SI prefix extensions. I spent a lot of time analyzing the article while blissfully unaware of its flaws (hey, I was a beginner), so I think I know what Joyce/Halm meant. In pataphysical tradition, Joyce notices this: * Take the Italian words for seven (sette) and eight (otto). * Prepend them with the letters Z and Y (zette, yotto). These are, of course, the last two letters of the alphabet in reverse order. * Discard everything except the first syllable, and append an A (zetta, yotta). * You now have the SI prefixes "zetta-" (10^21) and "yotta-" (10^24). * We can extend this by applying the same process with the word for nine, "nove". Prepend the third letter from the end of the alphabet to get xove -> xova-. * The same applies for ten, W + "dieci" = "wieca-". Joyce uses "weica-" instead; either a typo or pronunciation aid. * Similarly, V + undici = unda-. * U + dodici = uda-. Here Joyce replaces the entire first vowel with U. * T + tredici = teda-. * S + quattordici = satta-. * R + quindici = rinda-. * Q + sedici = qeda-. * P + diciasette = pica-. * O + diciotto = oca-. * N + diciannove = nica-. etc. There's more to it, but I'm in a hurry. Hope this helps. you're.so. 22:05, April 30, 2014 (UTC) This was me when reading the article: Safe to say that this g function thing only gets anywhere when the number of arguments is a multiple of 3. WikiRigbyDude (talk) 12:33, May 1, 2014 (UTC)